A-LevelMathematicsMechanics9709/42 · Feb/Mar 2023 · Q15 Marks

A crate of mass 200kg is being pulled at constant speed along horizontal ground by a horizontal rope attached to a winch. The winch is working at a constant rate of 4.5kW and there is a constant resistance to the motion of the crate of magnitude 600N.

(a)Find the time that it takes for the crate to move a distance of 15 m.[2]
(b)The rope breaks after the crate has moved 15m. Find the time taken, after the rope breaks, for the crate to come to rest.[3]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2023). The mark or mark type is shown in brackets.

[M1] Use of power = ∆W / ∆t to get an equation in t. May see 600v =4500 ⇒v=7.5 followed by 7.5t=15.
[A1] t=2s
[*M1] Use of Newton's second law; 2 terms only.
[DM1] Use of constant acceleration to set up an equation that would lead to a positive t, e.g. v=u+at with their t =2 and their negative a (and possibly their 7.5 from (a)).
[A1] t = 2.5s

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, Feb/Mar 2023 Paper 4 Variant 2, question 1.

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